In humans, geometrical illusions are thought to reflect mechanisms that are usually helpful for seeing the world in a predictable manner. These mechanisms deceive us given the right set of circumstances, correcting visual input where a correction is not necessary. Investigations of non-human animals' susceptibility to geometrical illusions have yielded contradictory results, suggesting that the underlying mechanisms with which animals see the world may differ across species. In this review, we first collate studies showing that different species are susceptible to specific illusions in the same or reverse direction as humans. Based on a careful assessment of these findings, we then propose several ecological and anatomical factors that may affect how a species perceives illusory stimuli. We also consider the usefulness of this information for determining whether sight in different species might be more similar to human sight, being influenced by contextual information, or to how machines process and transmit information as programmed. Future testing in animals could provide new theoretical insights by focusing on establishing dissociations between stimuli that may or may not alter perception in a particular species. This information could improve our understanding of the mechanisms behind illusions, but also provide insight into how sight is subjectively experienced by different animals, and the degree to which vision is innate versus acquired, which is difficult to examine in humans.